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In accordance with the holographic principle， by calculating the entropy of the quantum field just on the event horizon of the Gibbons-Maeda dilaton black hole， the holographic entropy and the Bekenstein-Hawking entropy of the black hole are obtained. By using the non-commutative quantum field theory， the divergence of the state density near the event horizon in usual quantum field theory is removed and the ultraviolet cutoff in the heat gas method of black hole entropy is avoided.Using the residue theorem, the integral difficulty in the calculation is overcome and the results here are obtained quantitatively. The results show that black hole entropy is identical with the statistical entropy of the quantum states at the horizon. Black hole entropy may be obtained by calculating the quantum states only at the event horizon, and in the calculation the influences of quantum states outside the horizon should be avoided.
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Keywords:
- black hole entropy/
- holographic principle/
- event horizon/
- non-commutative quantum field theory
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